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A number consists of two digits. The sum of the digits is 9. If 63 is subtracted from the number its digits are interchanged. Find the number .

A number consists of two digits. The sum of the digits is 9. If 63 is subtracted from the number its digits are interchanged. Find the number . Correct Answer 81

Let X and Y be the digits of decimal and unit places respectively. So, the number is 10X + Y. If 63 is subtracted from the number, it becomes 10Y + X. Now, X + Y = 9 - - - - - - - (i) Again, 10X + Y - 63 = 10Y + X or, 10X - X + Y - 10Y = 63 or, 9X - 9Y = 63 or, X - Y = 63/9 or, X - Y = 7 - - - - - - (ii) [(i) + (ii)]>>   X + Y + X - Y = 9 + 7 or, 2X = 16 or, X = 8 So, 8 + Y = 9 or, Y = 9 - 8 = 1 So, the number is 81.

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